Chapter 11. Testing the estimates. Age structure.
1. Introduction
2. Observations observed
3. Matching by Paine method matching
4. Resampling resampling
5. Accounting for a mismatch mismatch
6. Previous structures 1967, 1977, 1985 previoustructures
7. Comparing with Ache and !Kung comparingAcheKung
8. History from age structure historyfromstruc
9. Discussion and conclusion discuss
Table Tables
Figures Figures
References References
1. Introduction.
In the last chapter we looked at several measures of the Hadza population shaped by fertility
and mortality and related to age structure. I compared them to values predicted by a population
simulation that used as input my estimates of Hadza fertility and mortality. Most of the matches
were very close. Two summary measures of age structure (average age of the population,
percentage of people aged under 20) were already compared with the predicted values in the last
chapter. In the present chapter I will look at the entire age structure, first to see how well it
matches the model predictions, then to see whether it tells us anything
about recent Hadza history. I again base the predictions on the assumption that the
Hadza population was stable during most of the latter part of the twentieth century.
Thus I assume that fertility and mortality and migration persisted at the estimated
levels for several decades or more. In chapters 8 and 9 I offered evidence in support of this
assumption.
2. Observed age structure.
Age structure can be observed in censuses, or any observation that includes the largest
possible sample with the least bias against certain ages. It requires that the ages of the individuals
counted can be determined to some degree of accuracy. We could use the household censuses, the
population register, or the people who came to be measured. As described in the last chapter for %
under age 20, I used the numbers of people of each age who came to be measured.
It is well known that household censuses undercount children, which would distort the age
structure. This is the case among the Hadza as elsewhere, children listed by mother in her interview
were sometimes not entered in her household by our field assistant. The anthropometry sessions
created an opportunity for a less biased sample as well as for a measurement independent of the
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data on which estimates of fertility and mortality were based. People were very eager to be
measured, and for their children to be measured, because everyone was paid equally with a large
cup of maize meal. Even reluctant children were recorded if not weighed and received their
payment “for trying”. Comparing these data with an age structure derived from the population
register suggests that a small number of 3 and 4 year olds may not have come to be measured. The
youngest children came because they ride in mother’s baby sling most of the day and it would have
required mother to make special arrangements not to bring the baby.
I scored the data by adding each year’s data together, as described in the last chapter. This is
similar to building an average structure for the 10 years over which we intensively weighed people.
If we wanted to work out an average structure we would add the 1990 ten year olds and the 1991
ten year olds, and the 1992 ten year olds, and so on, then divide by the number of censuses. I
simply omitted the division. Many individuals were counted in more than one census, and were
counted according to their current age each time they were seen. This generates some smoothing of
the age structure. Suppose there were unusually few 3 year olds in 1990. Those of them who turned
up to be measured in 1991 were scored as 4 year olds, along with any other 4 year olds, and so on,
for each census up to 2000. The historical deficit will work its way up the age structure as the years
go by, and it will be obscured by the inclusion of those who were 3 in 1991, and 3 in 1992. This
procedure is obviously not useful for tracing historical peaks and troughs, although if you tabulate
each year next to each other you can see troughs and peaks work their way up the ages. A further
smoothing is discussed below, the use of % below each age instead of % in each year of age or
larger age block.
Figure 11.1 shows the abridged age pyramid. Figure 11.2 shows the year by year observed
age structure (with the sexes combined) plotted with the structure predicted by the Hadza
population simulation. The immediate impact is the irregularity of the observed structure. It jumps
back and forward across the smooth predicted structure, though roughly following the inevitable
trend toward fewer people at higher ages. There are some particular periods where several age
groups fall above or below the line. These may indicate interesting historical deviations from
population stability (i.e. real short term changes in fertility at a particular time, or mortality to a
particular age group). Birth rates and death rates did vary from year to year but they showed no
simple secular trend. To use the observations as a test of the predictions from the assumption of
long term stability we clearly need a systematic method of testing which predictions provide the
best fit to the observations, and some way to smooth the data. Even with these aids, we need to
remember that the observed age structure is a snapshot, one most likely to suffer short term
variation at extremes of age, as one of the two 80 year olds dies, or as some chance run of years
with many births comes by.
3. Matching observed age structure to predicted age structure.
The criteria for choosing between a good match and a poor match seems to
have received relatively little attention in the anthropological literature, much more in the
archaeological literature. Even quite recent researchers seemed to have been satisfied by raw
statements of "a good match", even though Weiss (1973) had suggested a simple criterion for
matching age structures. An objective criterion for choosing the best model is needed.
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Commonsense tests contradict each other. Chi-squared goodness of fit shows the observed numbers
of people in each year of age as a poor fit, significantly departing from expected at p <.001 (90
degrees of freedom). Regression of observed on expected gives a beta coefficient .9559 with p =
3.96 E – 49, and adjusted r squared = .9127, implying that the predicted structure accounted for
91% of the variance in observed age structure. Regression is very insensitive to the varied
predictions tested below.
I have used two methods: Weiss’ (1973: 65) Index of Dissimilarity, the sum of the absolute
values of the differences between percent predicted in each year of age and the percent of those
observed who were in this age. The results are reported here.
I also used Paine's (1989) maximum likelihood estimation approach, to find
the model that best fits the observed age structure. This also compares predicted and observed % in
each year of life. The observed % is multiplied by the natural log of the predicted number. The
results for the years are summed. The smallest score is the best match. The first model will be the
age structure predicted by our estimates of ASF and mortality. Alternative models will be predicted
age structure when ASF is increased, or decreased by up to 25%, and when mortality (qx) is
increased or decreased by similar amounts.
These methods allowed me to choose a best fitting prediction, although it is very unlikely
that in the range of interest any of them differ significantly from each other. The best matches were
with slightly lower fertility than originally estimated. Structures generated by subtracting 5% to
10% from each age specific fertility gave the best fit (Figure 11.3). When ASF is reduced by 5%,
TFR is lowered to 5.970, and by 10% TFR is 5.656. Next I matched the observed age structure to
structures predicted by a series of levels of mortality, with fertility held constant at the original
estimated level. The best match was to a much increased level of mortality.
Even the Hadza pattern of migration, in which young women leave to marry Swahilis, only
very slightly changes the expected age structure. Matching the observed age structure to the
structure predicted by various levels of migration (emigration of 15-30 year old females) suggests
that even though this very slightly lowers the expected numbers of children, it does not account for
the shortage of young children that can be seen in figure 11.2. Reducing fertility, and increasing
mortality would mainly affect the numbers of children. I will discuss alternative reasons for a
shortage of children in the relatively short time covered by the observed age structure.
4. Resampling predicted and observed age structures.
I developed another way to compare structures using resampling. In this the data were
smoothed by expressing the structure as % of individuals below age x, a measure listed in the Coale
& Demeny models. The predicted structures were generated by my population simulation. The
observed structures was calculated from the anthropometry data used above, and 95% confidence
limits were generated by randomly resampling the individuals who arrived to be measured.
Confidence limits of the observations can be compared to model structures resulting from higher
and lower fertility and mortality levels. Resampling the subjects who determine fertility and
mortality allows one to also estimate the 95% confidence intervals for the predicted age structure.
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In Figure 11.5 I show the observed values with the predicted values. The match looks
extremely close, with slight deviations reflecting shortages of children and fifty year-olds. The
results of resampling show that the 95% confidence limits for predictions of age structure reach as
far as a 10% increase or decrease in fertility. Resampling the observations shows a similar width of
confidence limits. This is illustrated in figure 11.5 for the sexes combined. The graph shows the
observed value, the 95% confidence limits for the observation, and the values predicted by adding
or subtracting 10% to age specific fertility. The predicted value was omitted because it runs so
close to the observed value.
When I predicted structure from altered mortality levels the result was much less
encouraging (Figure 11.6). Changing mortality has much less effect on the curve of percent below
each age. Consequently the 95% confidence intervals for observed mortality are wider than
predictions from even 20% added to or subtracted from each qx. Matching age structure to model
was not a very sensitive test of the mortality estimates. We must accept the quite wide range of
uncertainty in our estimates (+- 10%), which may on the other hand mean that we do not have to
take the mismatches too negatively.
5. Accounting for the mismatches.
There are several possible reasons for a mismatch. The matchings suggests
that we see a very slightly older population than we had expected (in Table 10.1, 2 and 3 we saw
that average age of population for each sex is near the upper 95% of the predicted range). Plotting
the percentage in each year of age shows, first the jagged nature of the structure. This is likely to
arise from a mixture of age heaping (i.e. errors in age estimation, especially among the oldest) and
genuine year to year variation, some random some meaningful.
The estimate of observed age structure may be wrong. For example, we can
confirm that household lists undercount children when compared to numbers
arriving to be measured. Under enumeration of children is well known in censuses.
Perhaps more young children failed to come to be measured than we realized. Age
estimates could be wrong. Age heaping would decrease the match to all models.
Systematic over-estimation of the age of young children seems unlikely in the
context of repeat visits and the averaging of age structure across those visits.
The observed age structure is also a short term “snapshot”, even with the smoothing effect
of my accumulating samples from the seven visits in the 1990s. Plotting the matches shows that
most of the mismatch arises from two periods: there are too few small children, and too few adults
aged 50-60. I will discuss the 50-60 year olds below but the shortage of small children is curious.
Although there was no statistically significant secular trend in birth rate, the observed structure
looks as if there may have been fewer births than usual in the late 1990s, or more births than usual
in the early 1990s. The better fit to predictions that assume lower fertility than I had estimated
might be misleading. It might be due to this run of lower birth rates. The loss of children from the
late 1986 measles epidemic shows in the age structure. There were also unusually few births dated
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to 1986. Perhaps interviewed women omitted the children who were born and died in 1986 – 1987,
or perhaps the illness affected everyone enough to briefly lower the birth rate.
The assumption of a stable population may be wrong. We have seen that fertility and
mortality vary year to year. There must always be variation in fertility and mortality from year to
year and even over strings of years. There might also be a steady trend toward increase or decrease
in fertility or mortality. I could see no clear evidence for such trends in the Hadza data and the age
structures of Dyson (1977 on data from 1967) and Lars Smith (1977 data) do not suggest any such
trend.
There is also a small amount of emigration, which I attempted to measure in
chapter 5. The departure of some young women, and loss of their offspring in every generation
could have mimicked the effect of lower fertility by everyone. The population model is able to
include the observed emigration of young women and return of older women. At the observed rate
(young women leaving at .3% per year, and returning later at .15%) the match of predicted to
observed structure is almost imperceptibly improved. At a rate of emigration 1% per year the match
for observed fertility and mortality is improved but to a trivial extent.
6. Previous structure data (1967, 1977, 1985)
If fertility and mortality remained approximately stable for long enough during
the 20th century, we might also observe similar age structures at different points during
the century. There are data available from before our 1990-2000 anthropometry
observations. We previously reported the structure in our 1985 census. But before that
Lars Smith conducted a rather thorough census in 1977, and Dyson (1977) reported the age
structure observed in 1967. Here we compare what they found with what we predict for a
stable population.
Age structure in 1967.
Dyson (1977) presented Hadza age structure in his Table 1, based on age estimates
provided in the field by James Woodburn and John Bennett, who were members of the
International Biological Program field team in 1966 and 1967. Their age estimates were
not as systematically derived as ours were but Woodburn had worked with the Hadza
since 1959 and had known many of the people individually for some years, and Bennett
was a physician with wide experience in East Africa. Dyson's table is reproduced in
Table 11.1. Dyson's sample is much smaller than ours so we combine the sexes for 1967
and in Figure 11.7 show the result with our observed 95th percentiles for males and
females. Although the 1967 data points wander across the 1990-2000 picture it would be
hard to argue that the 1967 age structure differed in a consistent way from the recent
structure.
The high data points for people beyond age 50 probably arise because the age estimates
were erroneously compressed, several of the people classified as aged 50-64 were
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probably older, some aged 65-69, and a few 70 -74 and so on just as today. The apparent
shortage of teenagers and young adults (age groups 10-14 and 15-19) is interesting. When the sexes
are plotted separately the shortage appears to apply to young men and even more to young women.
Perhaps there were reasons why people of this age group were not recorded (perhaps they were
away in the bush, still away attending school, travelling about, or just uncooperative). The shortage
consists of people who would have been aged between a little under 10 to a little under 20 (born
1957 – 1946) at the formation of the Yaeda settlement in 1964.
Age structure in 1977.
Lars Smith's census in dry season 1977 was very extensive, and included anthropometry but
he did not record detailed age estimates. We tabulate this population against our later estimates of
the year of birth of the individuals in the 1977 census. We had made estimates for many of those
who had died by the time our study began in 1985. Figures 11.8 a and b show the results for
females and males respectively plotted with the 95 percentile limits of the values predicted from
our fertility and mortality estimates for 1985-2000. Smith's sample fall mostly within the predicted
limits, females tending to more often
overlap the upper limit, males more often approach the lower limit.
Age structure in 1985.
Figure 11.9a and b shows the age structure of people recorded in our 1985 census,
computed using our final age estimates. The female age structure falls mostly within the predicted
95 percentiles but the male age structure does not.
The 1985 men are the only comparison in which the data persuasively fall outside the
predicted range. We should be reluctant to conclude that this exception is very meaningful. The
1985 male Hadza data seem to show a shortage of 20 year olds (born 1955-1965). Young men are
the most mobile segment of the population and may be poorly represented by our household lists.
While the data points fall outside the 95th percentile, they do not track as low as the !Kung age
structure (see below).
There are extremely rough indications of a quite young age structure in the early
literature. We began the fertility chapter with a quote from Cooper (1945 fieldwork) on
the large numbers of children. Obst commented on the proportion of children in 1911.
First at Baragu near Yaeda, a camp which he claimed included people who identified
themselves as Isanzu, he recorded 15 men, 18 women, and 22 children. Those who
claimed "pure Hadza ancestry" comprised 7 men, 7 women, and 11 children. If we
assume he defines children as aged up to age 16 (as seems quite likely where he discusses
age changes in skin color), these give us 40 and 44 % up to age 16. This is uncannily
close to our predicted low and high 95 percentiles of 41 - 45.5%. Even if we move the
age limit for childhood up or down a couple of years, Obst's figures do not suggest a
radical departure from the age structure expected and observed at the end of the century.
Though very limited, these early reports gives no reason for suspecting a radically
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different age structure from that observed since 1967.
7. Comparing Hadza age structure to predicted age structure of Ache and !Kung.
We can get a wider perspective on the Hadza age structure by comparing it with
other hunter-gatherer populations. The Ache and the !Kung are the most comprehensively
studied. !Kung age structure can be represented, according to Howell (1979) by Coale &
Demeny's model West 5 with rate of increase zero. Howell showed that !Kung
population up to the 1960s closely matched Coale & Demeny model West 5, with a very
low rate of increase. Howell p214 table 11.1 using net reproductive rate and length of
generation, calculates intrinsic rate of natural increase as .0026, and on p 218-219 reports
.0016 as the mean of ten simulations. Coale & Demeny list only r = 0 and r = 5 per
thousand (.005) so we used the figures for r = 0 in West 5 and read age structure and the
other measures direct from Coale & Demeny page 59. These predict a percentage under
age 20 well beyond that predicted by adding or subtracting 10% to Hadza fertility or
mortality.
Hill & Hurtado (1996) present yearly age-specific fertility (1996: 261Table 8.1) and
mortality (1996:196, Table 6.1) for the Ache in the forest before settlement. These data are easily
substituted for Hadza data in the simulation program and predictions derived for all the same
variables. Hill & Hurtado (1996, p:136, note 5) also suggest West 5 as a good match to their
observed age structures, but with an intrinsic rate of increase of 25.0 per thousand. Although their
age structure apparently matches this model, and some measures of mortality that they offer in their
note 5 also apparently fit the rate of increase implied by their population register, the level of
mortality that they report in their life table does not. Level 5 gives an expectation of life at birth of
30 for females whereas H&H report (1996:Table 6.1) 37 years. Level West 7 matches their e0 much
better, and with a GRR of 4 gives a very similar age structure to W5 with r = 25. But their detailed
and careful reporting of fertility and mortality allows us to run these in our population simulation
and predict an age structure and age at death structure for the Ache in the forest period. We use our
predicted Ache age structure to compare with !Kung and Hadza but we have plotted it alongside
their chosen West 5 with r = 25 and the plots are very close indeed. Note that this implies that the
observed values that H&H used to select a model are very close to those that would be predicted
from
their reported fertility and mortality schedules if they were stable for some decades. H&H
remark that the structure suggests about 40 years of stability before contact. The Ache
study apparently passes the same tests as I am attempting for the Hadza study.
Figures 11.10 a & b show for females, and males respectively, the observed Hadza age
structure observed in the anthropometry sample and compare this to the age structures
predicted for Ache and !Kung. The Hadza data fall clearly between the predicted
structures of the other populations. The 95% confidence limits of the Hadza observations just reach
the Ache levels and barely overlap the !Kung levels. It looks as if we can say that the Hadza values
lie somewhere between the Ache and the !Kung, and are different from these populations. This is
also true for all the measures shown in Tables 10.1, 10.2, 10.3.
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8. Fluctuations in Hadza age structure: Age structures and population history.
A more interesting use of age structures is as a way to trace historical events.
We might wish to test for an effect of a major change in lifestyle, such as a lasting
settlement, where people give up a mobile forager lifestyle for a less mobile life with
a mixed economy. Thus Hill & Hurtado (1996:149 Fig 4.10) can show the effects of high
mortality after contact on subsequent Ache age pyramids. Penningon & Harpending
(1993:51) suggest that Herero age structure shows the persistence across at least two
generations of effects of the Herero expulsion in 1904 from German South-West Africa (Namibia).
The age structure of the !Kung in the 1960s, could be examined for
effects of the apparent decrease in mortality. Paine (2000) shows that in medieval
Europe the plague left traces in the age at death structure for up to 50 years.
In the case of the Hadza we have no abrupt change in the last 50-100 years
that affected the whole population. But I have been interested in looking for a
trace of the high infant mortality that some Hadza informants associate with the
1964 settlement scheme. We might wonder whether the series of settlement
attempts, or the gradual encroachment by people with other economies, left a small
but persisting trace in the age structure as would be seen for instance if the Hadza
population began to move from increasing to decreasing. However, our attempts to look at
the history of Hadza fertility and mortality suggested substantial stability.
There are no massive anomalies in the Hadza age pyramid such as can be
seen in the Ache and Herero age pyramids. There is no consistent informant or
visitor report to suggest that there should be, there is no indication of a major
perturbation since the Maasai wars late in the 19th century. Can we see traces of
lesser perturbations? We must ignore the fluctuations among the oldest people, the
samples are small, and obvious age heaping can be seen from 1945 to 1920.
I have noticed apparent shortages of people in some age groups. Because informants had
told us that the time of the 1964 settlement at Yaeda was a time of many child deaths, I looked for a
dip in the age structure that might reflect these losses. I have seen none, in fact it is possible to
argue there is a slight excess of people born at that time (ages around 35 in Figure 11.2). To judge
from the Mono settlement in 1990 there may well have been a burst of births as the Yaeda food
supplies took effect. Without altering mortality rates this would have increased the absolute
number of child deaths that informants had witnessed. Instead there are indications of a shortage of
people, especially women, aged 40-50 in 2000. I mentioned it above as a shortage visible in
Dyson’s age structure (the people missing from Dyson’s age structure would be aged 43-54 in
2000. Two post hoc explanations can be offered. These people were born between 1946 and 1957.
There was a widespread and severe drought in 1949 (Baker 1974, Brooke 1967), although it does
not show in the Mbulu rainfall records in Meindertsma (1997: Fig 1.8). Perhaps this led to a
decrease in the number of births (as in 1998 after the total failure of rain in 1997), and/or an
increase in deaths. Another explanation would note that these people were aged 8-18 at the time of
the Yaeda and Munguli settlements. That the shortfall comprises more women than men may imply
that a larger than usual number of Hadza girls married Swahilis and left Hadza country at that time.
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They would be relatively unlikely to have entered our population register. A shortfall of people in
any particular year may mean fewer were born that year but it could reflect events that befell them
at any time between birth and observation. The shortfall in people born in 1986 probably reflects
mortality due to measles in the epidemic that followed a brief settlement attempt at Yaeda in that
year.
Age structure in 1999, estimated from the population register shows much
year to year variation. But it is too easy to see a deviation in age structure and find
an explanation for it. Having seen a significant shortfall in births in 1998 after failed
rains in 1997 (Chapter 8), it was easy to notice shortfalls in the age structure that coincided with or
immediately followed drought years commented on in the
literature (eg 1949, 1961, 1991-93). But regression of population deviation with
the long series of rainfall records from Mbulu shows no tendency for lower than
expected numbers to occur in years with lower rainfall, nor in the year following
low rainfall. In fact the data show a significant tendency for years of high rainfall to
be under-represented in the age structure. In a year with much rain, either fewer
births occur, or more of the children die, or both (regression b = 0.4059, p = .002,
r^2 = 16%). The literature (cited in Chapter 3) reports increased deaths from malaria during years
of high rainfall (supposedly good years for Mosquitos). Harpending (1976) noted higher child
mortality among !Kung living near the Okavango swamp than far from it. In 1998 a decrease in
child deaths is reported with high rainfall in Tanzania (Lindsay et al 2000). Those authors suggest
that the extremes of downpour and flash flooding may have swept away large numbers of Mosquito
larvae. My result must be considered very provisional, for instance, we do not even know whether
the rainfall figures given in Meindertsma are by calendar year (January to December) or rain year
(August to July).
9. Summary and Conclusion.
Measured as percent of people below age x, the observed age structure fits the predicted
age structure very well. The 95% confidence limits of the observations (obtained by resampling)
correspond to the structure given by about 10 % more, or ten percent less fertility. Matching
percent of people in each year of age gave a better match to structure predicted from fertility minus
5 or 10% than to predicted fertility. Holding fertility constant at the predicted level, the best match
is to the structure predicted by rather higher than observed mortality. Including a small amount of
emigration to the population simulation only very slightly improves the match between observed
structure and structure predicted by observed fertility and mortality. The tests continue to roughly
support the accuracy of my estimates of fertility and mortality and their stability.
Two historically significant deviations can be proposed, and a third mooted. The brief
settlement attempt in late 1986 led to a measles outbreak in which a number of children died. This
shows quite strikingly in the age structure. It seems to have been accompanied by a brief drop in
fertility. A shortage of people who were aged 8 – 18 in the peak years of the settlement at Yaeda in
the 1960s can be seen making its way through all the structures up to 2000. I suggest that this
implies that a significant number of young Hadza left at that time, for instance to marry Swahilis
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and never entered our population register. The lower than expected number of young children in the
2000 age structure could have resulted partly from the deaths in the 1986 measles epidemic, and
partly from a decline in the birth rate in the late 1990s. Logistic regression on the annual record of
births of the interviewed women shows that group of years 1996-2000 had a just significantly lower
probability of a birth to these women (b = –0.2258 p .04 Odds Ratio 0.80 (.64-.99)) and no
comparable length previous period was significantly different from the excluded years. Marlowe
and his students may be able to show us whether this heralded a lasting decline in the fertility and
rate of increase of the Hadza population.
Discussion: How many old people?
The most stubborn myth about hunter – gatherers is that there were no old people. Every
modern study with careful age estimation has shown a significant percentage of older people.
21.5% of Hadza women were aged over 40, 15.2% over 50, and 7.5% over 60. Even among the
Agta, with an excellent schedule of historical events for age estimation, and with very low life
expectancy at birth of 24.3 years, 6.8% of its people were aged over 45 in 1950 (Early & Headland
1998). Twenty four of every 100 Agta born survived to 50 (the expected survivorship for C&D
models West 3 or 4). In my 2002 paper I showed that Hadza, !Kung, and Ache women’s life
expectancy at age 45 was a further 21 years. Every study of living people, and people who had
written records, some more ancient than many of the archaeological populations, resembled modern
people in the presence of quite old people with some living into their 70s and 80s. An elderly
population could result from a declining population but neither the !Kung, the Ache, the Hadza, or
the Agta were declining, they were increasing rapidly, which should lower the proportion of old
people.
The myth gets its continued impetus from the contradiction between data on recorded
people and interpretations of bone collections. Bone collections show us portions of the age at
death distribution. They do not directly show us the age structure of people alive at the time. But
even if we realize this, some of them give very strange age at death distributions of a pattern seen in
few other species. Palaeodemographers (archaeologists who try to study demography of prehistoric
populations) have critically examined their procedures at many levels. They have investigated the
validity of methods for attaching an age at death to a bone; the problems of missing infants and
differences in preservation (the young and the old decay faster, Walker et al. 1988). An important
development is the distinction between “attritional” and “catastrophic” assemblages.
Palaeodemographers no longer necessarily support the view that there were “no old people”.
Howell (1982) pointed out that the age structure originally proposed for the Libben
population gave a very unfavorable dependency ratio. She asked who would be feeding and caring
for the children, implying that with so few caretakers child mortality would increase and fertility
decline. Ignoring parental care allows projection methods to model sustainable populations with
huge mortality from 30 onward, and all dead by 45. Later we will return to the issue of population
dynamics with and without adult helpers.
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In Hawkes & Blurton Jones (2005) we suggested that one important source of the
stubbornness of the myth was misunderstanding the implications of low life expectancy at birth.
Low life expectancy at birth is always due to very high infant and child mortality. Low life
expectancy does not necessarily signal early death among the over 40s. I will return to this topic in
the next chapter, on age at death distribution.
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Tables
Table 11.1. Dyson’s Table 1. The Hadza Age / Sex Distribution in 1966-67.
Age group
0
5
10
15
20
25
30
35
40
45
50
55
60+
Total
Males
27
52
26
13
10
19
21
18
20
22
7
3
5
243
Nick Blurton-Jones
%
11.1
21.4
10.7
5.3
4.1
7.8
8.6
7.4
8.2
9.1
2.9
1.2
2.1
Females
48
30
16
13
17
18
18
28
7
12
7
6
10
230
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%
20.8
13.0
6.9
5.6
7.4
7.8
7.8
12.2
3.0
5.2
3.0
2.6
4.3
Both
75
82
42
26
27
37
39
46
27
34
14
9
15
473
%
15.8
17.3
8.9
5.5
5.7
7.8
8.2
9.7
5.7
7.2
2.9
1.9
3.2
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Figures.
Figure 11.1 Abridged age pyramid
Figure 11.2 yearly age structure x predicted by pop simulation.
Figure 11.3. Matches to ASF weissASF
Figure 11.4 Matches to Mortality
Figure 11.5. Percent below age x observed, CI, predicted +-ASF
Figure 11.6 Percent below age x, observed x +- mortality adjmortality
Figure 11.7. Dyson’s 1977 age distribution compared to mine.dysonstr
Figure 11.8. Lars Smith’s 1977 age structures compared to mine a) female b) male.lars77males
Figure 11.9. 1985 age structure compared to mine.
Figure 11.10. Hadza observed age structure compared to Ache and !Kung. compareKungAche
Figure 11.1 Abridged age structure.
90
80
70
60
Age
50
40
30
20
10
0
-500
-400
-300
-200
-100
0
100
200
300
400
500
N females - N males
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Figure 11.2. Yearly age structure. Percent in year of age, observed, and predicted from estimated
fertility and mortality.
0.05
0.045
0.04
0.035
% in age (f+m)
0.03
0.025
0.02
0.015
0.01
0.005
0
0
10
20
30
40
50
60
70
80
90
100
age
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Figure 11.3. Weiss dissimilarity score matching observed age structure to values predicted by
different adjustments to fertility.
Scatterplot of dissimilarity vs asfadjust
0.23
dissimilarity
0.22
0.21
0.20
0.19
0.18
-30
-20
-10
0
10
20
asfadjust
Minitab-for-plotting-Weiss-11-9-3.mpj
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Figure 11.4. Weiss dissimilarity score matching observed age structure to values predicted by
different adjustments to mortality.
0.204
0.202
0.2
dissimilarity index
0.198
0.196
0.194
0.192
0.19
0.188
-30
-20
-10
0
10
20
30
Adjustment to mortality
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Figure 11.5. Percent below age x. 95% confidence intervals for observations and predictions. Sexes
combined.
1.2
1
% below age x
0.8
metry%bothbelow
pcbbelw00
pcbbelow-10
pcbbelow+10
lo bth % belw
hi bth %belw
0.6
0.4
0.2
0
0
10
20
30
40
50
60
70
80
90
100
age
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Figure 11.6. 95% confindence intervals for observed age structure x adjusted mortality. Percent
below age x.
1.2
1
% below age x
0.8
metry%bothbelow
lo bth % belw
hi bth %belw
b % blw +20
b %blw-20
0.6
0.4
0.2
0
0
10
20
30
40
50
60
70
80
90
100
age
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Figure 11.7. Age structure reported by Dyson for the 1967 Hadza population plotted alongside our
predicted 95 percentile values for males and females in the 1990s.
120
100
% below age x
80
m pred lo
m pred hi
f pred lo
f pred hi
Dyson both
60
40
20
0
0
10
20
30
40
50
60
70
80
90
100
age x
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Figure 11.8 a and b. Female age structure in Lars Smith’s 1977 census plotted alongside 95
percentiles of our predicted age structure for the 1990s.
120
100
% below age x
80
1977 % f below
f pred lo
f pred hi
60
40
20
0
0
10
20
30
40
50
60
70
80
90
100
age x
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Figure 11.8b. Male age structure in Lars Smith’s 1977 census plotted alongside 95 percentiles of
our predicted age structure for the 1990s.
120
100
% below age x
80
1977 % f below
f pred lo
f pred hi
60
40
20
0
0
10
20
30
40
50
60
70
80
90
100
age x
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Figure 11.9 a. 1985 structure x predicted range. a females..
Female age structure in 1985 using final age estimates
120
100
% below age x
80
% f below
f pred lo
f pred hi
60
40
20
0
0
10
20
30
40
50
60
70
80
90
100
age x
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Figure 11.9 b. 1985 structure x predicted range. Males from 1985 census lists.
1985 male age structure using final age estimates
120
100
% below age x
80
% m below
m pred lo
m pred hi
60
40
20
0
0
10
20
30
40
50
60
70
80
90
100
age x
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Figure 11.10 a. Ninety-five percentiles of observed Hadza female age structure alongside Ache
predicted age structure and !Kung female age structure represented by coale & Demeny model
West 5 r = 0.
120
100
% below age x
80
Ache fem
W5 r0 fem
f mtry lo
f mtry hi
60
40
20
0
0
10
20
30
40
50
60
70
80
90
100
age x
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Figure 11.10b. Ninety-five percentiles of observed male age structure alongside Ache predicted
age structure and !Kung female age structure represented by coale & Demeny model West 5 r = 0.
120
100
% below age x
80
Ache % below m
W5r0 male
m mtry lo
m mtry hi
60
40
20
0
0
10
20
30
40
50
60
70
80
90
100
age x
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